An improvement of the exponential differencing scheme for solving the convection-diffusion equation

Abstract

In order to reduce false diffusion in numerical solutions of the convection-diffusion equation both in orthogonal and body-fitted coordinates, a simple differencing scheme suitable to the control-volume method is proposed. The scheme is based on the one-dimensional exact solution of the convection-diffusion equation with constant coefficients and constant source term. Accuracy of the proposed scheme is assessed through a number of test situations of pure convective and convective-diffusive transport with known exact solutions. Results show relevant accuracy improvements with respect to the popular exponential differencing scheme (EDS). The proposed scheme is simple, accurate and easy to implement in existing codes based on the EDS. The extension to three-dimensional situations is straightforward.